The first determination of a stellar parallax was made by F.
Annual parallax is the angle between the direction in which a star appears from the earth and the direction in which it appears from the centre of the sun.
Maskelyne's first contribution to astronomical literature was "A Proposal for Discovering the Annual Parallax of Sirius," published in 1760 (Phil.
The most important of these, the sun's mean parallax, was at that time subject to considerable uncertainty.
To obtain the true parallax, the mean parallax of the comparison stars must be added to this relative parallax.
From a fresh discussion of the transits of Venus in 1761 and 1769 he deduced (1822-1824) a solar parallax of 8" 57, long accepted as authoritative.
It consisted essentially in the adoption of Delauny's final numerical expressions for longitude, latitude and parallax, with a symbolic term attached to each number, the value of which was to be determined by substitution in the equations of motion.
The most brilliant star of this constellation, a-Aquilae or Altair, has a parallax of 0.23", and consequently is about eight times as bright as the sun; q-Aquilae is a short-period variable, while Nova Aquilae is a " temporary " or " new " star, discovered by Mrs Fleming of Harvard in 1899.
The parallax 8.5776" found by Encke was therefore accepted without question, and was employed in the Nautical Almanac from 1834 to 1869.
Doubt was first thrown on the accuracy of this number by an announcement from Hansen in 1862 that the observed parallactic inequality of the moon was irreconcilable with the accepted value of the solar parallax, and indicated the much larger value 8.97".
' The most remarkable feature of the discussion since 1862 is that the successive examinations of the subject have led to a continually diminishing value, so that at the present time it seems possible that the actual parallax of the sun is almost as near to the old value of Encke as to that which first replaced it.
By the American photographs the distances between the centres of Venus and the sun, and the angles between the line adjoining the centres and the meridian, could be separately measured and a separate result for the parallax derived from each.
Had the internal contacts alone been used, which many astronomers would have considered the proper course, the result would have been 8.776" In 1877 Sir David Gill organized an expedition to the island of Ascension to observe the parallax of Mars with the heliometer.
The effect of parallax could be obtained as well as by observing from two different stations; in fact the rotation of the earth carried the observer himself round a parallel of latitude, so that the comparison of his own morning and evening observations could be used as if they had been made at different stations.
The failure of the method based on transits of Venus led to an international effort carried out on the initiative of Sir David Gill to measure the parallax by observations on those minor planets which approach nearest the earth.
The results were for the solar parallax 7r: The general mean result was 8.802".
On these occasions the actual parallax would be six times greater than that of the sun, and could therefore be measured with much greater precision than in the case of any other planet.
Advantage was taken of the occasion to make photographic measures for parallax at various points of the earth on a very large scale.
The corresponding value of the solar parallax is 8.782".
The determination of the solar parallax through the parallactic inequality of the moon's motion also involves two elements - one of observation, the other of purely mathematical theory.
The following may be taken as the most probable values of the solar parallax, as derived independently by the five methods we have described: From measures of parallax.
Probably no general agreement could now be reached on a statement more definite than this; the last result may be left out of consideration, and the value of the solar parallax is probably contained between the limits 8.77" and 8.80."
These pairs of observations have shown a parallax from which the elevation of the objects above the earth, the lengths and directions of their courses, &c. could be computed.
The instrument so altered was in use at the Cape Observatory from March 1881 till 1887 in determining the parallax of some of the more interesting southern stars.
In determinations of stellar or solar parallax, comparison stars, symmetrically situated with respect to the object whose parallax is sought, should be employed, in which case the instantaneous scale-value may be regarded as an unknown quantity which can be derived in the process of the computation of the results.
Examples of this mode of procedure will be found, in the case of stellar parallax in the Mem.
Parts I and 2; and in the case of planetary parallax in the Mem.
Dr Chase's measures with the Yale heliometer indicated for it, in 1894, a parallax of about o" ï¿½ 035; 2 and it must, accordingly, be of nearly four times the total brightness of Sirius, while its aerial lustre exceeds seventyfold that of the solar photosphere.
He also reduced the solar parallax to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.
In 1680 Jean Picard, in his Voyage d'Uranibourg, stated, as a result of ten years' observations, that Polaris, or the Pole Star, exhibited variations in its position amounting to 40" annually; some astronomers endeavoured to explain this by parallax, but these attempts were futile, for the motion was at variance with that which parallax would occasion.
This motion is evidently not due to parallax, for, in this case, the maximum range should be between the June and December positions; neither was it due to observational errors.
It is, the orbit and periodic time is known, and also the parallax, the masses of the stars can be found.
(If only the relative orbit is known, the sum of the masses can be determined; but if absolute positions of one component have been observed, both masses can be determined separately.) But even when, as in most cases, the parallax is unknown or uncertain, the ratio of the brightness to the mass can be accurately found.
If 7r be the parallax, and R the radius of the earth's orbit, the distance of the star is R/sin ir.
The determination of stellar parallaxes is a matter of great difficulty on account of the minuteness of the angle to be measured, for in no case does the parallax amount to I"; moreover, there is always an added difficulty in determining an annual change of position, for seasonal instrumental changes are liable to give rise to a spurious effect which will also have an annual period.
He found for it a parallax of o 35" a value which agrees well with more modern determinations.
Henderson at the Cape of Good Hope measured the parallax of a Centauri, but his resulting value 1" was considerably too high.
More accurate determinations have shown that this star, which is the third brightest star in the heavens, has a parallax of 0.75", this indicates that its distance is 25,000,000,000,000 m.
The quantity determined by these methods is the relative parallax between the star measured and the stars with which it is compared.
It is, however, fair to assume that the comparison stars will rarely have a parallax as great as o oi "; for it must be remembered that it is quite the exception for a star taken at random to have an appreciable parallax; particularly if a star has an ordinarily small proper motion, it is likely to be very distant.
In the table are collected the parallaxes and other data of all stars for which the most probable value of the parallax exceeds 0.20".
To convert parallaxes into distance we may remember that a parallax of i" denotes a distance of 182 billion miles, or 206,000 times the distance of the sun from the earth.